中文摘要：

该文针对二元假设检验问题，首先在贝叶斯准则的基础上，分析了最小化贝叶斯代价所对应的最优噪声，将贝叶斯代价的最小化问题等价为虚警概率和／或检测概率的最优化。其次，在保证一定虚警概率和检测概率的前提下，建立起能同时改善检测概率和虚警概率的模型。然后分别给出当检测概率一定时虚警概率最小和虚警概率一定时检测概率最大这两种极限情况下对应的最优加性噪声，并对其进行线性凸组合以获得模型所需的最优加性噪声，进一步分析并证明了该模型能够成立的充分条件。再次，获得先验概率已知和未知两种情况下最小化贝叶斯代价时所对应的加性噪声，且当先验知识发生改变时，该算法只需调整加性噪声中一个可变参数即可获得相应的最优贝叶斯代价。最后，结合具体的检测问题，通过仿真验证了所提算法的有效性。

英文摘要：

The optimal noise that minimizes Bayes risk for a binary hypothesis testing problem is analyzed firstly. As a result, the minimization of Bayes risk can be equivalent as the optimization of the detection probability （PD） and/or false alarm probability （PFA） . Secondly, a noise enhanced model, which can increase PD and decrease PFA simultaneously, is established under the premise of maintaining predefined PFA and PD. Then the optimal additional noise of this model is obtained by a convex combination of two optimal noises of two limit cases, which are the minimization of PFA with maintaining the predefined PD and the maximization of PD with maintaining the predefined PFA, respectively. Furthermore, the sufficient conditions for this model are given. What＇s more, the additive noise that minimizes the Bayes risk is determined when the prior probabilities are known or not, and the corresponding additive noise can be obtained by recalculating a parameter only if the prior information changes. Finally, the availability of algorithm is proved through the simulation combined with a specific detection example.